Peter Linz Edition 4 Exercise 4.3 Question 16 (Page No. 123)

Question

Is the following language regular?

  $L=$ {$w_1cw_2:w_1,w_2∈$ {$a,b$}$^*,w_1\neq w_2$}.

Answer 1

It Is Not Regular Language

 

But If C ia also Belong To { a,b }* Then It Is Regular Language

Because We Assume W1 And W2 Are NuLL(  ε  )

And Language Reduce To 

L= { C : C ∈ { a,b }*   } Which is Regular

Comments

Can we assume that both w1 and w2 to be null as they are supposed to be different .